Simple linear formulation for magnetostimulation specific to MRI gradient coils

Abstract

A simple linear formulation for magnetostimulation thresholds specific to MRI gradient coils is derived based on established hyperbolic electrostimulation strength vs. duration relations. Thresholds are derived in terms of the gradient excursion required to cause stimulation, and it is demonstrated that the threshold curve is a linear function of the gradient switching time. A parameter β is introduced as being fundamental in the evaluation of gradient coil stimulation. β is a map of the induced electric field per unit gradient slew rate, and can be calculated directly from the gradient coil wire pattern. Consideration of β alone is sufficient to compare stimulation thresholds between different gradient coil designs, as well as to evaluate the expected dependency of stimulation threshold on position within the gradient coil. The linear gradient threshold curve is characterized by two parameters: SRmin and δGmin. SRmin is the slope of the threshold curve and represents the minimum slew rate required to cause stimulation in the limit of infinite gradient strength. δGmin is the vertical axis intercept of the curve and represents the minimum gradient excursion required to cause stimulation in the limit of infinite slew rate. Both SRmin and δGmin are functions of both β and the standard tissue parameters Er (rheobase) and τc (chronaxie time). The ease with which both the gradient system performance and the stimulation thresholds can be plotted on the same axes is noted and is used to introduce the concept of a piece-wise linear operational limit curve for a gradient system. © 2001 Wiley-Liss, Inc.